数列＜an＞中,a3=2,a7=1.数列＜1/(an+1)＞是等差数列,3Q

Question

数列＜an＞中,a3=2,a7=1.数列＜1/(an+1)＞是等差数列,3Q

Answer 1

bn=1/(an+1) b3=1/(a3+1)=1/3 b7=1/(a7+1)=1/2 数列＜bn＞是等差数列,公差d=(1/2-1/3)/4=1/24 b1=b3-2d=1/3-1/12=1/4 bn=1/4+(n-1)/24 1/(an+1)=1/4+(n-1)/24=(n+5)/24 an=24/(n+5)-1(n=1,2,……)